Unai Emery has identified the 24-year-old as a possible replacement for Ramsey, whose deal at the Emirates expires at the end of the season.
Ramsey will become eligible to sign a pre-contract with an overseas club in January if a new deal hasn’t been agreed with the Gunners before then, and Real Madrid have been heavily linked with a move for the Welsh international.
However, Emery could look to offload Ramsey in January to help raise funds for the Napoli’s Zielinski, who is valued at around £30million.
Italian publication Mediaset, as suggested by The Sun, claims Emery sees Zielinski as a player who could enhance the Gunners current squad and add goals from midfield.
The Poland international moved to Napoli from Udinese in 2016 for £14million and has netted 11 goals in 74 appearances since.
Napoli will be desperate to keep Zielinski as they look to dethrone Juventus, who beat them to the Serie A title last season.
It will take a huge bid from Arsenal for Napoli to consider selling Zielinski this January as he still has just under three years left to run on his current deal.
Liverpool have also been credited with some interest in the Napoli star.